Sensitivity comparison of absorption and grating-based phase tomography of paraffin-embedded human brain tissue

Advances in high-resolution hard X-ray computed tomography have led to the ﬁeld of virtual histology to complement histopathological analyses. Phase-contrast modalities have been favored because, for soft tissues, the real part of the refractive index is orders of magnitude greater than the imaginary part. Nevertheless, absorption-contrast measurements of parafﬁn-embedded tissues have provided exceptionally high contrast combined with a submicron resolution. In this work, we present a quantitative comparison of phase tomography using synchrotron radiation-based X-ray double grating interferometry and conventional synchrotron radiation-based computed tomography in the context of histopathologically relevant parafﬁn-embedded human brain tissue. We determine the complex refractive index and compare the contrast-to-noise ratio (CNR) of each modality, account-ing for the spatial resolution and optimizing the photon energy for absorption tomography. We demonstrate that the CNR in the phase modality is 1.6 times higher than the photon-energy optimized and spatial resolution-matched absorption measurements. We predict, however, that a further optimized phase tomography will provide a CNR gain of 4. This study seeks to boost the discussion of the relative merits of phase and absorption modalities in the context of parafﬁn-embedded tissues for virtual histology, highlighting the importance of optimization procedures for the two complementary modes and the trade-off between spatial and density resolution, not to mention the disparity in data acquisition and processing. In conclusion, we report a quantitative measurement of the refractive index for a specimen of medical relevance. We show that a substantial part of the CNR gain from XDGI to absorption can be compensated by the loss in the spatial resolution from grating interferometry. We also show that when the photon energy is selected to optimize absorption measurements, the CNR gain from XDGI is substantially smaller. This plays an important role because it is techni-cally easier to optimize the photon energy for an absorption measurement than for a grating interferometer. Our results indicate that for parafﬁn-embedded specimens, absorption tomography is a very attrac-tive time-, cost-, and effort-effective approach. Depending on the speciﬁc application, these advantages can play a deﬁning role, as in the case of time-critical biopsy evaluations or high-throughput animal experiments that require the processing of hundreds of samples. These results emphasize the complex relationship between CNR and the spatial resolution as well as the importance of considering the optimization procedures for each technique when comparing imaging modalities.

Since the invention of the Bonse-Hart interferometer, 1 X-ray phase contrast imaging has been preferentially considered for light elements, i.e., the main constituents of human tissues, for which the decrement of the real part of the refractive index d is three orders of magnitude larger than the imaginary part b at photon energies on the order of 10 keV. 2 Therefore, researchers estimated that phase-contrast tomography could reach a hundred to thousand times greater sensitivity than absorption-contrast tomography. 3,4 Pioneering tomography studies with hard X-rays revealed that not only the widely used absorption-contrast and the newer phase-contrast imaging techniques provide complementary information but also phase imaging yields a substantially better contrast-to-noise ratio (CNR) than absorption. During the last two decades, high-resolution tomography in the phase-contrast mode has enabled the visualization of individual cells 5 and even sub-cellular details 6,7 in the post mortem human brain. Highresolution X-ray phase-contrast tomography shows great promise for augmenting standard pathology in research and clinics with the socalled virtual histology. [8][9][10] Several experimental results, however, indicate that conventional X-ray absorption tomography provides comparable CNR to phase tomography for paraffin-embedded soft tissues, i.e., those used in typical histopathological analysis. For example, conventional tomography of the paraffin-embedded brain 11 and peripheral nerves 12 has yielded sufficient CNR to identify biological cells and related microstructures. Thus, it is still unclear which method is more effective for the visualization of anatomical features in human tissues in the context of virtual histology.
Consequently, the aim of the present tomography study is a quantitative comparison of the density resolution of absorption-and phase-contrast modalities in the case of histopathologically relevant biological specimens embedded in paraffin. To this end, part of a formalin-fixated and paraffin-embedded human cerebellum was three-dimensionally visualized by means of conventional synchrotron radiation-based microcomputed tomography (SRlCT) and doublegrating interferometry (XDGI). For a complete comparison, SRlCT data were also recorded at an optimized photon energy significantly lower for the chosen sample than the energy used for XDGI. The tomography datasets were rigidly registered, and the common volume was extracted to generate bivariate distributions to directly compare the CNR. Additionally, the absorption projections were filtered to compare the CNR of the modalities at an equal spatial resolution.
The human cerebellum specimen was selected with informed consent for scientific use. All the associated procedures were conducted in accordance with the Declaration of Helsinki and were approved by the ethics committee of the Medical School of the National and Kapodistrian University of Athens. The brain was extracted post mortem from a donated body and fixed in 4% histological-grade buffered paraformaldehyde. To allow for sufficient perfusion of solvents and liquid paraffin, 2-cm-thick cerebellum slices were produced, dehydrated in ascending ethanol solutions, transferred to xylene, and finally embedded in a paraffin/plastic polymer mixture, following the standard pathology procedure. Out of the obtained paraffin blocks, cylinders 6 mm in diameter were obtained by means of a stainless-steel punch.
The wavefront w immediately after passing through the specimen is given by projection approximation 13 wðx; y; zÞ ¼ wðx; y; 0Þ exp Àik This expression is equivalent to Beer's law, with the linear attenuation coefficient l ¼ 2kb. If a grating interferometer is placed behind the sample, the interference pattern fringes are shifted laterally by an angle a x given by the derivative of the wavefront phase shift a x ðx; yÞ ¼ @/ðx; yÞ @x ¼ @ @x ð dðx; y; zÞdz: Phase stepping allows for retrieval of a x , and reconstruction with a modified filter kernel allows for d-retrieval. 14,15 Phase and absorption tomography measurements using a photon energy of 20 keV, denoted DPC 20 and ABS 20, were performed at the Diamond Manchester Imaging Beamline [I13-2, Diamond Light Source (DLS), UK]. Additionally, an absorption tomography measurement at a photon energy of 10 keV, denoted ABS 10, was performed at the P05 beamline (PETRA III, DESY, Hamburg, Germany), a facility operated by the Helmholtz-Zentrum Geesthacht.
This study comprises at least seven parameters. The impact of these parameters has been considered, allowing for a comparison of the three dominant factors: (i) the contrast mechanisms, (ii) the selection of photon energy for absorption, and (iii) the balancing of the spatial resolution.
For a homogeneous specimen of diameter D with a linear attenuation coefficient l(E), the optimal photon energy for an absorption measurement is found by setting l(E) Â D ¼ 2. 16 For inhomogenous specimens, a lower value is usually chosen. This value was 0.3 and 1.6 for ABS 20 and ABS 10, respectively, indicating that 10 keV is closer to the optimum efficiency criteria.
The XDGI setup consisted of a beam-splitting absorption grating and an equivalent analyzer grating with a periodicity of p 1 ¼ p 2 ¼ 7 lm and a gold structure height of 70 lm. The ideal transmission of this interferometer is 25%. An inter-grating distance of 80 cm was used, corresponding to the first fractional Talbot order. Five phase step images were recorded per projection. The setup had a mean visibility of 35%.
Between DPC 20 and ABS 20, the gratings and the water bath (used to avoid phase wrapping) were removed, the exposure time reduced, and the detector distance set to 7 cm. This was the minimum distance without changing the rotation stage. For ABS 10, the specimen-detector distance was 1 cm to reduce edge enhancement. All projections were 2 Â 2 binned to improve the signal and ease data handling. 17 Table I lists the acquisition parameters.
The phase retrieval for DPC 20 was performed by applying a pixel-wise Fourier analysis. 14 The tomographic reconstruction relied on the standard filtered back-projection algorithm, which is implemented in Matlab (The MathWorks, Inc., Natick, USA), using a modified filter kernel (Hilbert transform). 15 Prior to reconstruction, Gaussian filters with r ¼ 1.52 and r ¼ 1.48 pixels were applied to the projections of ABS 20 and ABS 10, respectively. This filter size matched p 2 , which is the lower resolution limit of the phase measurement. 14 The approximately equal spatial resolution was confirmed by EHD SciCam, EHD Imaging GmbH, Damme, Germany. c Olympus Corporation, Tokyo, Japan. d the selected line profiles, where the number of pixels defining the edges between paraffin and the molecular layer for the filtered absorptioncontrast datasets was less than or equal to that for the phase-contrast dataset.
To obtain meaningful bivariate histograms, also known as joint histograms, the data have to be precisely registered. Therefore, an affine three-dimensional registration was performed by means of an algorithm to maximize mutual information, [18][19][20] with ABS 20 selected as a reference and DPC 20 or ABS 10 as the floating dataset. Tricubic interpolation was used for visualization, while the nearest neighbor interpolation was used for the analysis in order to avoid smoothing of the floating datasets. Figure 1 shows a slice through the registered reconstructions of (a) DPC 20, (b) filtered and (c) unfiltered ABS 10, and (d) filtered and (e) unfiltered ABS 20. Related zoom-in views are given on the right to better visualize the (anatomical) features, i.e., the paraffin (PA), the molecular layer (ML), and the granular layer (GL). Purkinje cells can be identified between the ML and GL, see, e.g., bright dots in the zoomed view of (b). The white matter (WM) is found on the right side of each slice, with grayscale values between ML and GL.
Joint histograms from common volumes of tomography datasets allow for segmentation of specimen components 21,22 and direct comparison of the density resolution. Figure 2 shows the joint histograms of DPC 20 and filtered ABS 10 and filtered ABS 20. The histograms fit with a four-Gaussian model were chosen to match the number of features. The center and the width of the Gaussians are superimposed onto the joint histogram as a visual aid. The superior CNR of DPC 20 compared to the filtered ABS 20 is clear from the broadening of the Gaussian peaks. This is less evident for DPC 20 compared to ABS 10.
Equally sized regions of interest were selected within homogeneous areas characteristic of each (anatomical) feature in order to determine their index of refraction and the CNR. Paraffin was used as the reference material, as the surrounding medium was water for DPC 20 and air for ABS 20 and ABS 10. The measured Dd 6 r d (or Db 6 r b ) values and the mean CNRs are shown in Table II. Both the histogram fits from Fig. 2 Table II indicate a nearly linear relationship between the real and imaginary parts of the refractive index, with Dd/Db % 700 at 20 keV.

and the values from
We define the Relative Contrast Gain (RCG) as the ratio of the CNR of the phase dataset over various absorption datasets. [23][24][25] The filtered datasets have a similar spatial resolution, and therefore, the RCG indicates the image quality improvement of phase contrast compared to absorption contrast. The RCG depends not only on Dd/Db but also on the sensitivity of the grating interferometer and on the tomographic reconstruction. Table II shows the CNR and RCG for each dataset. Higher RCG values indicate a larger advantage of phase contrast over the dataset in question. Filtering increased the CNR by a factor of around 14 (5) for ABS 20 (ABS 10), underlining the importance of a comparison at an equal spatial resolution. The current study should initiate a detailed experimental study to understand the improvement of tomographic data quality by Gaussian filtering.
The absorption datasets, particularly ABS 20, where the sampledetector distance was larger, show edge enhancement, and thus, the phase retrieval proposed by Paganin et al. was applied. 26

ARTICLE
scitation.org/journal/apl and Paganin's method produced similar image quality although the sample-detector distance was not optimized for Paganin's method. 26 The Gaussian filter was selected for this study because it requires no a priori knowledge of the refractive index and, unlike, e.g., binning, allows for fine control of the kernel size in order to match the spatial resolution between the datasets. Photon energy optimization plays a large role in reducing the RCG (or increasing CNR) for the absorption measurements. Db increased by a factor of over 7 by decreasing the photon energy from 20 keV to 10 keV, creating a larger difference in absorption, while still allowing sufficient transmission for counting statistics. Adjusting the photon energy greatly impacts the count rate due to the details of the insertion device, optics, and the detection system at each synchrotron facility. In our case, the count rate is more than tripled for the measurement at lower photon energy. Together, the higher count rate and the lower energy provided a CNR improvement of around 7 (2.5) for the unfiltered (filtered) datasets. Typically, photon energy is not optimized in XDGI measurements because gratings are designed for operation at a few specific energies.
For larger specimens, the criteria proposed by Grodzins suggest a higher optimal energy. 16 For example, an entire rat brain (assuming a diameter of 12.5 mm) has an optimal photon energy of around 15 keV, while for a human brain (diameter 100 mm), it is around 50 keV. Therefore, it is not always the case that taking absorption at lower energies than the phase will improve the CNR. Nevertheless, most grating interferometers are designed for one specific energy, which may not be close to the optimal energy for absorption or phase measurements of a given specimen. The optimization of photon energy for grating-based phase contrast has not been experimentally studied. This study focuses on the case of 6 mm punches, a typical size for high resolution computed tomography experiments with effective pixel sizes in the micrometer range and fields-of-view of several millimeters.
The sensitivity of a grating interferometer can be described by the minimum resolvable deflection angle 27 Thus, the effect of increased counts can be extrapolated by the ffiffiffiffi N p term, with the caveat that low count rates may lead to reduced visibility or a degraded spatial resolution due to mechanical instabilities over longer acquisition times. The relationship between the period of the second grating p 2 , the inter-grating distance d, and the visibility V is more complex. The visibility depends on the transverse coherence length, l c ¼ kL/s (photon wavelength k, source-sample distance L, and source size s), p 2 , and the Talbot order n 28 This allows us to extrapolate to a grating interferometer with better-adapted parameters, e.g., a p-shifting first grating and a 2.4 lm analyzer grating period with the visibility around 45% at the 11th Talbot order, corresponding to 485 mm for the 19 keV design energy (see Ref. 9). Compared to our setup, this would provide a sensitivity gain of ffiffi ffi 2 p from increased transmission, 2.9 from p 2 , and 0.6 from d. The exact visibility cannot be calculated without knowing the coherence properties of the beamline, the motor stability, and the grating quality; however, our setup would be favored due to the smaller np 2 (i.e., more robust against transverse incoherence). The spatial resolution is limited to at least twice p 2 , and thus, the optimized setup would allow for CNR gain from filtering. We predict that an optimized grating interferometer could reasonably achieve four times greater sensitivity. This image quality improvement over absorption is still far less than the Dd/Db ratio and should be weighed against the more complicated and timeconsuming acquisition of XDGI.  In conclusion, we report a quantitative measurement of the refractive index for a specimen of medical relevance. We show that a substantial part of the CNR gain from XDGI to absorption can be compensated by the loss in the spatial resolution from grating interferometry. We also show that when the photon energy is selected to optimize absorption measurements, the CNR gain from XDGI is substantially smaller. This plays an important role because it is technically easier to optimize the photon energy for an absorption measurement than for a grating interferometer. Our results indicate that for paraffin-embedded specimens, absorption tomography is a very attractive time-, cost-, and effort-effective approach. Depending on the specific application, these advantages can play a defining role, as in the case of time-critical biopsy evaluations or high-throughput animal experiments that require the processing of hundreds of samples. These results emphasize the complex relationship between CNR and the spatial resolution as well as the importance of considering the optimization procedures for each technique when comparing imaging modalities.